Energy-dense rechargeable batteries for electronics, transportation and grid energy storage commonly suffer from low performance at low temperatures and safety problems at high temperatures. At low temperatures, especially subfreezing temperatures, rechargeable batteries, especially lithium-ion batteries, exhibit very low power performance and low energy due to sluggish electrochemical kinetics and transport processes occurring in the battery cell. At high temperatures, lithium-ion batteries have a strong tendency to undergo thermal runaway, leading to significant hazards. There is a need for rechargeable batteries with improved performance at low temperatures and/or improved high-temperature safety.